Round your answers to two decimal points, and don’t round intermediate calculations.
Problem 1.
Suppose that you have decided to fund a three-year liability with a portfolio consisting of positions in a two year zero-coupon bond (2YR) and a four-year zero-coupon bond (4YR). The current interest rate level is 10%.
a) Compute the price of both bonds.
b) Since our liability is a three-year liability, we want to immunize our portfolio by duration matching.
Set up the portfolio, describing how many dollars you have to invest into each bond.
c) Immediately after you make your initial purchases, rates fall to 8%. If you do not rebalance your
portfolio, what is your realized yield after three years?
d) What is the duration of the portfolio after the drop in interest rates without rebalancing?
e) How would you have to rebalance your portfolio?
Problem 2.
A 30-year maturity bond has an 8.5% coupon rate, paid annually. It sells today for $871.17. A 20-year
maturity bond has an 8.0% coupon rate, also paid annually. It sells today for $894.50. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 9.5% and 15-year maturity bonds will sell at yields of 9.0%. Because the yield curve is upward sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 7%.
a) Calculate the annualized expected rate of return of the 30-year bond over the 5-year period.
b) Calculate the annualized expected rate of return of the 20-year bond over the 5-year period.
Problem 3.
Consider a 7.4% coupon bond with face value of $1,000, making annual coupon payments, that has three years until maturity.
a) Find the duration of the bond if the yield to maturity is 7.4%.
b) Repeat your calculation, but instead consider a bond paying semiannually instead of annually.
Problem 4.
A five-year bond with a yield of 11% pays an 8% coupon at the end of each year.
a) What is the bond’s price?
b) What is the bond’s duration?
c) Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield.
d) Recalculate the bond’s price on the basis of a 10.8% per annum yield, and compare.
